What is the integral of (sqrt(x)-3/x)^2 ?

The integral of (sqrt(x)-3/x)^2 is -9/x-12sqrt(x)+(x^2)/2+C

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integral of (sqrt(x)-3/x)^2

\int (x - \frac{3}{x})^{2} d x

- \frac{9}{x} - 12 x + \frac{x ^{2}}{2} + C

Solution steps

\int (x - \frac{3}{x})^{2} d x

Expand

(x - \frac{3}{x})^{2} : \frac{9}{x ^{2}} - \frac{6}{x ^{\frac{1}{2}}} + x

= \int \frac{9}{x ^{2}} - \frac{6}{x ^{\frac{1}{2}}} + x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{9}{x ^{2}} d x - \int \frac{6}{x ^{\frac{1}{2}}} d x + \int x d x

\int \frac{9}{x ^{2}} d x = - \frac{9}{x}

\int \frac{6}{x ^{\frac{1}{2}}} d x = 12 x^{\frac{1}{2}}

\int x d x = \frac{x ^{2}}{2}

= - \frac{9}{x} - 12 x^{\frac{1}{2}} + \frac{x ^{2}}{2}

Apply radical rule:

= - \frac{9}{x} - 12 x + \frac{x ^{2}}{2}

Add a constant to the solution

= - \frac{9}{x} - 12 x + \frac{x ^{2}}{2} + C

\int \frac{3}{1 - 2 x} d x

\int cos (2 π x) d x

\frac{\partial}{\partial z} (x y sin (z))

\frac{d y}{d x} = (\frac{x}{2000}) - (\frac{y}{5000}), y (0) = 0

x \to 5 lim (- (\frac{x + 1}{x - 5}))

What is the integral of (sqrt(x)-3/x)^2 ?
The integral of (sqrt(x)-3/x)^2 is -9/x-12sqrt(x)+(x^2)/2+C